418 research outputs found
Distances on a one-dimensional lattice from noncommutative geometry
In the following paper we continue the work of Bimonte-Lizzi-Sparano on
distances on a one dimensional lattice. We succeed in proving analytically the
exact formulae for such distances. We find that the distance to an even point
on the lattice is the geometrical average of the ``predecessor'' and
``successor'' distances to the neighbouring odd points.Comment: LaTeX file, few minor typos corrected, 9 page
Nernst Effect as a Signature of Quantum Fluctuations in Quasi-1D Superconductors
We study a model for the transverse thermoelectric response due to quantum
superconducting fluctuations in a two-leg Josephson ladder, subject to a
perpendicular magnetic field B and a transverse temperature gradient. The
off-diagonal Peltier coefficient (\alpha_{xy}) and the Nernst effect are
evaluated as functions of B and the temperature T. The Nernst effect is found
to exhibit a prominent peak close to the superconductor-insulator transition
(SIT), which becomes progressively enhanced at low T. In addition, we derive a
relation to diamagnetic response: \alpha_{xy}= -M/T_0, where M is the
equilibrium magnetization and T_0 a plasma energy in the superconducting legs.Comment: An extended (and hopefully more comprehensible) version of an earlier
postin
Phase separation during film growth
A diffusion equation describing phase separation during co‐deposition of a binary alloy is derived, and solved in the limit of dominant surface diffusion. Linear stability analysis yields results similar to bulk spinodal decomposition, except that long, and possibly all, wavelength are stabilized. Decomposition into two phases is investigated by solving the diffusion equation for lamellar and cylindrical symmetry. For the lamellar geometry, typically observed for near‐equal volume fractions, the diffusion equation does not yield wavelength selection criteria. These can be obtained if free energy minimization is assumed. For the cylindrical geometry, solutions for small volume fractions yield domain dimensions proportional to the deposition‐rate dependent surface diffusion length.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71165/2/JAPIAU-72-2-442-1.pd
"This is my unicorn, Fluffy": Personalizing frozen vision-language representations
Large Vision & Language models pretrained on web-scale data provide
representations that are invaluable for numerous V&L problems. However, it is
unclear how they can be used for reasoning about user-specific visual concepts
in unstructured language. This problem arises in multiple domains, from
personalized image retrieval to personalized interaction with smart devices. We
introduce a new learning setup called Personalized Vision & Language (PerVL)
with two new benchmark datasets for retrieving and segmenting user-specific
"personalized" concepts "in the wild". In PerVL, one should learn personalized
concepts (1) independently of the downstream task (2) allowing a pretrained
model to reason about them with free language, and (3) does not require
personalized negative examples. We propose an architecture for solving PerVL
that operates by extending the input vocabulary of a pretrained model with new
word embeddings for the new personalized concepts. The model can then reason
about them by simply using them in a sentence. We demonstrate that our approach
learns personalized visual concepts from a few examples and can effectively
apply them in image retrieval and semantic segmentation using rich textual
queries
Computing the Hessenberg matrix associated with a self-similar measure
We introduce in this paper a method to calculate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G. Mantica to calculate the Jacobi matrix associated with a sum of measures from the Jacobi matrices of each of the measures.
We apply this method to approximate the Hessenberg matrix associated with a self-similar measure and compare it with the result obtained by a former method for self-similar measures which uses a fixed point theorem for moment matrices. Results are given for a series of classical examples of self-similar measures.
Finally, we also apply the method introduced in this paper to some examples of sums of (not self-similar) measures obtaining the exact value of the sections of the Hessenberg matrix
Pythagoras' Theorem on a 2D-Lattice from a "Natural" Dirac Operator and Connes' Distance Formula
One of the key ingredients of A. Connes' noncommutative geometry is a
generalized Dirac operator which induces a metric(Connes' distance) on the
state space. We generalize such a Dirac operator devised by A. Dimakis et al,
whose Connes' distance recovers the linear distance on a 1D lattice, into 2D
lattice. This Dirac operator being "naturally" defined has the so-called "local
eigenvalue property" and induces Euclidean distance on this 2D lattice. This
kind of Dirac operator can be generalized into any higher dimensional lattices.Comment: Latex 11pages, no figure
Superconductor-Insulator Magneto-Oscillations in Superconducting Strips
The magnetoresistance of thin superconducting strips subject to a
perpendicular magnetic field B and low temperatures T manifests a sequence of
alternating superconductor-insulator transitions (SIT). We study this
phenomenon within a quasi one-dimensional (1D) model for the quantum dynamics
of vortices in a line-junction between coupled parallel SC wires, at parameters
close to their SIT. Mapping the vortex system to 1D Fermions at a chemical
potential dictated by B, we find that a quantum phase transition of the Ising
type occurs at critical values of the vortex filling, from a SC phase near
integer filling to an insulator near 1/2-filling. For T->0, the resulting
magnetoresistance R(B) exhibits oscillations similar to the experimental
observation.Comment: 4 pages + a bit (4 in the journal), 1 figure. This is the published
version (appeared as Editor's Suggestion, June 30 2011
Alternating Superconductor--Insulator Transport Characteristics in a Quantum Vortex Chain
Experimental studies of magnetoresistance in thin superconducting strips
subject to a perpendicular magnetic field B exhibit a multitude of transitions,
from superconductor to insulator and vice versa alternately. Motivated by this
observation, we study a theoretical model for the transport properties of a
ladder--like superconducting device close to a superconductor--insulator
transition. In this regime, strong quantum fluctuations dominate the dynamics
of the vortex chain forming along the device. Utilizing a mapping of the vortex
system at low energies to one-dimensional (1D) Fermions at a chemical potential
dictated by B, we find that a quantum phase transition of the Ising type occurs
at critical values of the vortex filling, from a superconducting phase near
integer filling to an insulator near 1/2-filling. The current--voltage (I-V)
characteristics of the weakly disordered device in the presence of a d.c.
current bias I is evaluated, and investigated as a function of B, I, the
temperature T and the disorder strength. In the Ohmic regime (I/e << T), the
resulting magnetoresistance R(B) exhibits oscillations similar to the
experimental observation. More generally, we find that the I-V characteristics
of the system manifests a dramatically distinct behavior in the superconducting
and insulating regimes.Comment: 10 pages, 3 figures. arXiv admin note: substantial text overlap with
arXiv:1010.066
Dirac Operators and the Calculation of the Connes Metric on arbitrary (Infinite) Graphs
As an outgrowth of our investigation of non-regular spaces within the context
of quantum gravity and non-commutative geometry, we develop a graph Hilbert
space framework on arbitrary (infinite) graphs and use it to study spectral
properties of graph-Laplacians and graph-Dirac-operators. We define a spectral
triplet sharing most of the properties of what Connes calls a spectral triple.
With the help of this scheme we derive an explicit expression for the
Connes-distance function on general directed or undirected graphs. We derive a
series of apriori estimates and calculate it for a variety of examples of
graphs. As a possibly interesting aside, we show that the natural setting of
approaching such problems may be the framework of (non-)linear programming or
optimization. We compare our results (arrived at within our particular
framework) with the results of other authors and show that the seeming
differences depend on the use of different graph-geometries and/or Dirac
operators.Comment: 27 pages, Latex, comlementary to an earlier paper, general treatment
of directed and undirected graphs, in section 4 a series of general results
and estimates concerning the Connes Distance on graphs together with examples
and numerical estimate
A genetic contribution from the Far East into Ashkenazi Jews via the ancient Silk Road
Contemporary Jews retain a genetic imprint from their Near Eastern ancestry, but obtained substantial genetic components from their neighboring populations during their history. Whether they received any genetic contribution from the Far East remains unknown, but frequent communication with the Chinese has been observed since the Silk Road period. To address this issue, mitochondrial DNA (mtDNA) variation from 55,595 Eurasians are analyzed. The existence of some eastern Eurasian haplotypes in eastern Ashkenazi Jews supports an East Asian genetic contribution, likely from Chinese. Further evidence indicates that this connection can be attributed to a gene flow event that occurred less than 1.4 kilo-years ago (kya), which falls within the time frame of the Silk Road scenario and fits well with historical records and archaeological discoveries. This observed genetic contribution from Chinese to Ashkenazi Jews demonstrates that the historical exchange between Ashkenazim and the Far East was not confined to the cultural sphere but also extended to an exchange of genes
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